243 research outputs found
Small-time asymptotics for basket options -- the bi-variate SABR model and the hyperbolic heat kernel on
We compute a sharp small-time estimate for the price of a basket call under a
bi-variate SABR model with both parameters equal to and three
correlation parameters, which extends the work of Bayer,Friz&Laurence [BFL14]
for the multivariate Black-Scholes flat vol model. The result follows from the
heat kernel on hyperbolic space for combined with the Bellaiche [Bel81]
heat kernel expansion and Laplace's method, and we give numerical results which
corroborate our asymptotic formulae. Similar to the Black-Scholes case, we find
that there is a phase transition from one "most-likely" path to two most-likely
paths beyond some critical .Comment: 24 pages, 10 figure
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